The incident took place last night when Jogendra Singh (35) and his wife Renu (30) were boarding a crowded compartment of Jammu Tavi-Sealdah Express train.
The couple slipped on the tracks and were struck by the moving train, they said.
Their children, Kartik (12) and Krishna (6) were still at the platform when the train moved.
The victims were going to Roorkee when the mishap took place.
The bodies have been sent for post-mortem.